# Different types of waves

What is the difference between a progressive wave and a plane progressive wave? I realise that a progressive wave is one where waves are generated continuously, all the particles of the medium oscillate continuously (unlike stationary waves in which there are nodes), and the amplitude of each particle is the same, while the phases differ.
I read around, and I found that plane progressive waves are ones where the particles oscillate continuously, but simple harmonically.

My question is, how do the particles of progressive waves oscillate, if not simple harmonically? From what I could infer, if they didn't oscillate simple harmonically, the amplitude of each particle would be different, which basically means it's not a progressive wave at all.

Whether or not the waves are simple harmonic is, in my view, a separate issue, but as I'm sure you're aware, any waveform can be analysed into a sum of simple harmonic oscillations. The term 'plane progressive wave' is often used loosely to mean plane, progressive, simple harmonic wave, for which the displacement, $\mathbf{y}$, at a point $\mathbf{r}$ may be written $$\mathbf{y}=\mathbf{A}\ cos(\mathbf{k}.\mathbf{r} -\omega t + \phi)$$ in which $\mathbf{A}$ is the amplitude, $\mathbf{k}$ is the wave vector, a vector of magnitude $\frac{2 \pi}{\lambda}$ pointing in the direction of propagation of the waves and $\phi$ is a phase constant, allowing the wave to have any phase we choose at t = 0.